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Temporal cliques admit sparse spanners
Abstract Let G=(V, E) be an undirected graph on n vertices and λ: E→ 2 N a map** that
assigns to every edge a non-empty set of integer labels (discrete times when the edge is …
assigns to every edge a non-empty set of integer labels (discrete times when the edge is …
Simple, strict, proper, happy: A study of reachability in temporal graphs
A Casteigts, T Corsini, W Sarkar - Theoretical Computer Science, 2024 - Elsevier
Dynamic networks are a complex subject. Not only do they inherit the complexity of static
networks (as a particular case); they are also sensitive to definitional subtleties that are a …
networks (as a particular case); they are also sensitive to definitional subtleties that are a …
Cops & robber on periodic temporal graphs: Characterization and improved bounds
We study the classical Cops and Robber game when the cops and the robber move on an
infinite periodic sequence of graphs on the same set V of n vertices: in round t, the topology …
infinite periodic sequence of graphs on the same set V of n vertices: in round t, the topology …
Locating a black hole in a dynamic ring
In networked environments supporting mobile agents, a pressing problem is the presence of
network sites harmful for the agents. In this paper we consider the danger posed by a node …
network sites harmful for the agents. In this paper we consider the danger posed by a node …
In search of the lost tree: Hardness and relaxation of spanning trees in temporal graphs
A Casteigts, T Corsini - International Colloquium on Structural Information …, 2024 - Springer
A graph whose edges only appear at certain points in time is called a temporal graph
(among other names). These graphs are temporally connected if all pairs of vertices are …
(among other names). These graphs are temporally connected if all pairs of vertices are …
Cop numbers of periodic graphs
A\emph {periodic graph} ${\cal G}=(G_0, G_1, G_2,\dots) $ with period $ p $ is an infinite
periodic sequence of graphs $ G_i= G_ {i+ p}=(V, E_i) $, where $ i\geq 0$. The graph …
periodic sequence of graphs $ G_i= G_ {i+ p}=(V, E_i) $, where $ i\geq 0$. The graph …
Black hole search in dynamic cactus graph
We study the problem of black hole search by a set of mobile agents, where the underlying
graph is a dynamic cactus. A black hole is a dangerous vertex in the graph that eliminates …
graph is a dynamic cactus. A black hole is a dangerous vertex in the graph that eliminates …
Black hole search in dynamic rings
In this paper, we start the investigation of distributed computing by mobile agents in
dangerous dynamic networks. The danger is posed by the presence in the network of a …
dangerous dynamic networks. The danger is posed by the presence in the network of a …
Black hole search in dynamic rings: The scattered case
In this paper we investigate the problem of searching for a black hole in a dynamic graph by
a set of scattered agents (ie, the agents start from arbitrary locations of the graph). The black …
a set of scattered agents (ie, the agents start from arbitrary locations of the graph). The black …
Exploration of dynamic networks: tight bounds on the number of agents
We consider, for the first time, the exploration of dynamic graphs of arbitrary unknown
topology. We study the number of agents necessary and sufficient to explore such graphs …
topology. We study the number of agents necessary and sufficient to explore such graphs …